Question

In a paper bag, 7 of the 15 marbles are yellow. In a cloth bag, 2 of the 15 marbles are yellow. If Tim randomly draws one marble from each bag, what is the probability that they are both yellow?

Answer 1

Answer :

$\frac{7}{15}$×$\frac{2}{15}$ = $\frac{14}{225}$

Step-by-step explanation:

P($Event_{1}$) = choosing yellow marble from paper bag = $\frac{favourable outcomes}{possible outcomes}$ = $\frac{7}{15}$

P($Event_{2}$) = choosing yellow marble from cloth bag = $\frac{favourable outcomes}{possible outcomes}$ = $\frac{2}{15}$

∵ Resultant outcome is dependent upon both the events and both events are independent from each other, so we can apply intersection rule [ P(A∩B)=P(A)×P(B) ] here

∴ Probability ( Both marbles are yellow) = P($Event_{1}$) × P($Event_{2}$) = $\frac{7}{15}$ × $\frac{2}{15}$